Peter goes to the market looking to purchase a bag of sugar. The mass of 1 bag is 8 kg. How many grams of sugar are in the bag?

In this concept, you will learn to identify equivalent metric units of mass.

### Equivalent Metric Units for Mass

The **metric system** is an international system of measurement that uses the base units of meter, kilograms, and seconds to measure length, mass, and time. Mass is measured using grams. One of the benefits of using metric units is the use of metric prefixes. The prefixes also represent powers of ten, which make finding equivalent units easy. Here are some of the metric units of mass.

Metric Unit |
kilogram |
hectogram |
dekagram |
gram |
decigram |
centigram |
milligram |

Symbol | kg | hg | dag | g | dg | cg | mg |

Number | 1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 |

The most commonly used units of mass are kilogram, gram, and milligram.

Of the three units, the kilogram is the largest and the milligram is the smallest. The prefix “kilo” means a thousand and “milli” means one-thousandths. A gram is the basic unit of mass. You can use equivalent units of mass to convert different units to the same unit for comparison. **Equivalent** means equal.

1 kilogram is equal to 1,000 grams. 1 milligram is equal to one-thousandths of a gram.

Note that to convert a larger unit to a smaller unit, multiply by a power of ten to move the decimal to the right.

Multiply by 1000 to convert 1 gram to milligrams.

Also note that to convert a smaller unit to a larger unit, divide by a power of ten to move the decimal to the left.

Divide by 1000 to convert 1 gram to kilograms.

Now try to convert 1 kilogram to milligrams.

You are converting a larger unit to a smaller unit, so multiply. You already know 1 kg equals 1,000 g.

Then, convert 1,000 grams to milligrams. Multiply the number of grams by 1,000 to convert grams to milligrams.

1 kilogram is equal to 1,000,000 milligram.

### Examples

#### Example 1

Earlier, you were given a problem about Peter at the market.

Peter wants to know how many grams are in an 8 kg bag of sugar. Convert 8 kg to grams.

First, figure out if you are converting from a smaller unit to a larger or a larger unit to a smaller unit. You are converting kilograms to grams, which is a larger unit to a smaller unit. You will have to multiply.

Then, convert kilograms to grams. Multiply 8 by 1,000.

There are 8,000 grams in 8 kilograms.

#### Example 2

Use the equivalent rates to convert units.

How many grams are in 18 kilograms?

First, figure out if you are converting from a smaller unit to a larger or a larger unit to a smaller unit. You are converting kilograms to grams, which is a larger unit to a smaller unit. You will have to multiply.

Then, multiply the number of kilograms by 1000 to convert kilograms to grams.

There are 18,000 grams in 18 kilograms.

**Convert each metric unit of mass to its equivalent.**

#### Example 3

First, figure out if you are converting from a smaller unit to a larger or a larger unit to a smaller unit. You are converting kilograms to grams, which is a larger unit to a smaller unit. You will have to multiply.

Then, convert kilograms to grams. Multiply 6 times 1000.

There are 6,000 grams in 6 kilograms.

#### Example 4

First, figure out if you are converting from a smaller unit to a larger or a larger unit to a smaller unit. You are converting grams to kilograms, which is a smaller unit to a larger unit. You will have to divide.

Then, convert kilograms to grams. Divide 3,000 by 1000.

\begin{align*}3,000 \ g\div 1,000 = 3 \ kg\end{align*}

There are 3 kilograms in 3,000 grams.

#### Example 5

First, figure out if you are converting from a smaller unit to a larger or a larger unit to a smaller unit. You are converting grams to milligrams, which is a larger unit to a smaller unit. You will have to multiply.

Then, convert grams to milligrams. Multiply 4 times 1000.

There are 4,000 milligrams in 4 grams.

### Review

Convert each metric unit of mass to its equivalent.

- 5 kg = _______ g
- 2000 g = _______ kg
- 2500 g = _______ kg
- 10 kg = _______ g
- 2000 mg = _______ g
- 30 g = _______ mg
- 4500 mg = _______ g
- 6.7 g = _______ mg
- 9 kg = _______ g
- 10 g = _______ kg
- 1 kg = _______ mg
- 5000 mg = _______ g
- 7500 g = _______ kg
- 8200 g = _______ kg
- 15 kg = _______ g
- 1600 g = _______ mg

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.17.